Capitalism **as we know it** is wholly dependent on organized coercion, such as that provided by the government. Without that organized coercion--private property rights protected by the state, contract rights enforced by the state... capitalism would be a pale shadow of itself. That is exactly right! I do not know why you contradict yourself next:
Would capitalism cease to exist? No. People would still trade. But they would be trading beads, not derivatives. Capitalism is defined by property rights, free trade is something else.
I have the, perhaps, quirky view that capitalism is an emergent property of human nature. People always have and always will trade. From that fact emerges private property and economic systems, great and small.
How and to what extent it emerges depends on context. The government and how it interacts with the market being a big part of the context, the judaeo-christian ethic being another.
So we have only a definitional quibble. What I am calling capitalism is somewhat broader than what you are calling it. It really matters not at all; we do not appear to disagree on substance.